One contribution of 11 to a Theme Issue 'Towards the virtual physiological human: mathematical and computational case studies'. Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

The architecture of the heart remains controversial despite extensive effort and recent advances in imaging techniques. Several opposing and non-mutually compatible models have been proposed to explain cardiac structure, and these models, although limited, have advanced the study and understanding of heart structure, function and development. We describe key areas of similarity and difference, highlight areas of contention and point to the important limitations of these models. Recent research in animal models on the nature, geometry and interaction of cardiac sheet structure allows unification of some seemingly conflicting features of the structural models. Intriguingly, evidence points to significant inter-individual structural variability (within constrained limits) in the canine, leading to the concept of a continuum (or distribution) of cardiac structures. This variability in heart structure partly explains the ongoing debate on myocardial architecture. These developments are used to construct an integrated description of cardiac structure unifying features of fibre, sheet and band architecture that provides a basis for (i) explaining cardiac electromechanics, (ii) computational simulations of cardiac physiology and (iii) designing interventions.

. Visualization and quantification of whole rat heart laminar structure using highspatial resolution contrast-enhanced MRI. Am J Physiol Heart Circ Physiol 302: H287-H298, 2012. First published October 21, 2011; doi:10.1152/ajpheart.00824.2011.-It has been shown by histology that cardiac myocytes are organized into laminae and this structure is important in function, both influencing the spread of electrical activation and enabling myocardial thickening in systole by laminar sliding. We have carried out high-spatial resolution three-dimensional MRI of the ventricular myolaminae of the entire volume of the isolated rat heart after contrast perfusion [dimeglumine gadopentate (Gd-DTPA)]. Four ex vivo rat hearts were perfused with Gd-DTPA and fixative and high-spatial resolution MRI was performed on a 9.4T MRI system. After MRI, cryosectioning followed by histology was performed. Images from MRI and histology were aligned, described, and quantitatively compared. In the three-dimensional MR images we directly show the presence of laminae and demonstrate that these are highly branching and are absent from much of the subepicardium. We visualized these MRI volumes to demonstrate laminar architecture and quantitatively demonstrated that the structural features observed are similar to those imaged in histology. We showed qualitatively and quantitatively that laminar architecture is similar in the four hearts. MRI can be used to image the laminar architecture of ex vivo hearts in three dimensions, and the images produced are qualitatively and quantitatively comparable with histology. We have demonstrated in the rat that: 1) laminar architecture is consistent between hearts; 2) myolaminae are absent from much of the subepicardium; and 3) although localized orthotropy is present throughout the myocardium, tracked myolaminae are branching structures and do not have a discrete identity. myocardium; magnetic resonance imaging; ventricles; small animal imaging MYOCARDIAL STRUCTURE IS CENTRALLY important to cardiac mechanical function in health and disease (6), and myolaminar sliding is thought to be the principle mechanism of myocardial thickening in systole (10). Myolaminar structure has recently been shown to substantially influence the spread of activation in the myocardium (8,20).The myocardium is structured as stacked laminae of myocytes 4 -6 cells thick (ϳ80 -120 m), also known as myolaminae or sheets (24). These laminae are organized together in a complex fashion in which there are some regions of abrupt transmural change in laminar organization. The long axes of the myocytes, which make up the laminae, have a regular helical organization: the orientation of their long axes (with respect to the cardiac short axis) varies through ϳ120°trans-murally from endocardium to epicardium (33). The average orientation of the long axes of neighboring myocytes is known as the fiber-orientation (16). The myocardium therefore has regular lower order fiber architecture, with a more irregular and locally distinct higher order laminar arc...

We have constructed computational models of canine ventricular cells and tissues, ultimately combining detailed tissue architecture and heterogeneous transmural electrophysiology. The heterogeneity is introduced by modifying the Hund-Rudy canine cell model in order to reproduce experimentally reported electrophysiological properties of endocardial, midmyocardial (M) and epicardial cells. These models are validated against experimental data for individual ionic current and action potential characteristics, and their rate dependencies. 1D and 3D heterogeneous virtual tissues are constructed, with detailed tissue architecture (anisotropy and orthotropy, due to fibre orientation and sheet structure) of the left ventricular wall wedge extracted from a diffusion tensor imaging data set. The models are used to study the effects of tissue heterogeneity and class III drugs on transmural propagation and tissue vulnerability to re-entry. We have determined relationships between the transmural dispersion of action potential duration (APD) and the vulnerable window in the 1D virtual ventricular wall, and demonstrated how changes in the transmural heterogeneity, and hence tissue vulnerability, can lead to generation of re-entry in the 3D ventricular wedge. Two class III drugs with opposite qualitative effects on transmural APD heterogeneity are considered: d-sotalol that increases transmural APD dispersion, and amiodarone that decreases it. Simulations with the 1D virtual ventricular wall show that under d-sotalol conditions the vulnerable window is substantially wider compared to amiodarone conditions, primarily in the epicardial region where unidirectional conduction block persists until the adjacent M cells are fully repolarised. Further simulations with the 3D ventricular wedge have shown that ectopic stimulation of the epicardial region results in generation of sustained re-entry under d-sotalol conditions, but not under amiodarone conditions or in control. Again, APD increase in M cells was identified as the major contributor to tissue vulnerability--re-entry was initiated primarily due to ectopic excitation propagating around the unidirectional conduction block in the M cell region. This suggests an electrophysiological mechanism for the anti- and proarrhythmic effects of the class III drugs: the relative safety of amiodarone in comparison to d-sotalol can be explained by relatively low transmural APD dispersion, and hence, a narrow vulnerable window and low probability of re-entry in the tissue.

Pulmonary hypertension provokes right heart failure and arrhythmias. Better understanding of the mechanisms underlying these arrhythmias is needed to facilitate new therapeutic approaches for the hypertensive, failing right ventricle (RV). The aim of our study was to identify the mechanisms generating arrhythmias in a model of RV failure induced by pulmonary hypertension. Rats were injected with monocrotaline to induce either RV hypertrophy or failure or with saline (control). ECGs were measured in conscious, unrestrained animals by telemetry. In isolated hearts, electrical activity was measured by optical mapping and myofiber orientation by diffusion tensor-MRI. Sarcoplasmic reticular Ca(2+) handling was studied in single myocytes. Compared with control animals, the T-wave of the ECG was prolonged and in three of seven heart failure animals, prominent T-wave alternans occurred. Discordant action potential (AP) alternans occurred in isolated failing hearts and Ca(2+) transient alternans in failing myocytes. In failing hearts, AP duration and dispersion were increased; conduction velocity and AP restitution were steeper. The latter was intrinsic to failing single myocytes. Failing hearts had greater fiber angle disarray; this correlated with AP duration. Failing myocytes had reduced sarco(endo)plasmic reticular Ca(2+)-ATPase activity, increased sarcoplasmic reticular Ca(2+)-release fraction, and increased Ca(2+) spark leak. In hypertrophied hearts and myocytes, dysfunctional adaptation had begun, but alternans did not develop. We conclude that increased electrical and structural heterogeneity and dysfunctional sarcoplasmic reticular Ca(2+) handling increased the probability of alternans, a proarrhythmic predictor of sudden cardiac death. These mechanisms are potential therapeutic targets for the correction of arrhythmias in hypertensive, failing RVs.

New findings

During non-steady-state exercise, dynamic changes in pulmonary oxygen uptake (VO₂pulm) are dissociated from skeletal muscle VO₂ (VO₂musc) by changes in lung and venous O₂ concentrations (CvO₂), and the dynamics and distribution of cardiac output (CO) between active muscle and remaining tissues (Qrem). Algorithms can compensate for fluctuations in lung O₂ stores, but the influences of CO and CvO₂ kinetics complicate estimation of VO₂musc from cardio-pulmonary measurements. We developed an algorithm to estimate VO₂musc kinetics from VO₂pulm and heart rate (HR) during exercise. 17 healthy volunteers (28 ± 7 years; 71 ± 12 kg; 7 females) performed incremental exercise using recumbent cycle ergometry (VO₂peak 52 ± 8 ml min(-1) kg(-1)). Participants completed a pseudo-random binary sequence (PRBS) test between 30 and 80 W. VO₂pulm and HR were measured, and CO was estimated from HR changes and steady-state stroke volume. VO₂musc was derived from a circulatory model and time series analyses, by solving for the unique combination of venous volume and the perfusion of non-exercising tissues that provided close to mono-exponential VO₂musc kinetics. Independent simulations showed that this approach recovered the VO₂musc time constant (τ) to within 7% (R(2) = 0.976). Estimates during PRBS were venous volume 2.96 ± 0.54 L; Qrem 3.63 ± 1.61 L min(-1); τHR 27 ± 11 s; τVO₂musc 33 ± 8 s; τVO₂pulm 43 ± 14 s; VO₂pulm time delay 19 ± 8 s. The combination of stochastic test signals, time series analyses, and a circulatory model permitted non-invasive estimates of VO₂musc kinetics. Large kinetic dissociations exist between muscular and pulmonary VO₂ during rapid exercise transients.

During exercise below the lactate threshold (LT), the rate of adjustment (τ) of pulmonary O 2 uptake (V O 2 ) is slowed when initiated from a raised work rate. Whether this is consequent to the intrinsic properties of newly recruited muscle fibres, slowed circulatory dynamics or the effects of a raised metabolism is not clear. We aimed to determine the influence of these factors on τV O 2 using combined in vivo and in silico approaches. Fifteen healthy men performed repeated 6 min bouts on a cycle ergometer with work rates residing between 20 W and 90% LT, consisting of the following: (1) two step increments in work rate (S1 and S2), one followed immediately by the other, equally bisecting 20 W to 90% LT; (2) two 20 W to 90% LT bouts separated by 30 s at 20 W to raise muscle oxygenation and pretransition metabolism (R1 and R2); and (3) two 20 W to 90% LT bouts separated by 12 min at 20 W allowing full recovery (F1 and F2). Pulmonary O 2 uptake was measured breath by breath by mass spectrometry and turbinometry, and quadriceps oxygenation using near-infrared spectroscopy. The influence of circulatory dynamics on the coupling of muscle and lung τV O 2 was assessed by computer simulations. The τV O 2 in R2 (32 ± 9 s) was not different (P > 0.05) from S2 (30 ± 10 s), but both were greater (P < 0.05) than S1 (20 ± 10 s) and the F control bouts (26 ± 10 s). The slowedV O 2 kinetics in R2 occurred despite muscle oxygenation being raised throughout, and could not be explained by slowed circulatory dynamics (τV O 2 predicted by simulations: S1 = R2 < S2). These data therefore suggest that the dynamics of muscle O 2 consumption are slowed when exercise is initiated from a less favourable energetic state.